On line arrangements in the hyperbolic plane

• Given a finite collection L of lines in the hyperbolic plane H, we denote by k = k(L) its Karzanov number, i.e., the maximal number of pairwise intersecting lines in L, and by C(L) and n = n(L) the set and the number, respectively, of those points at infinity that are incident with at least one line from L. By using purely combinatorial properties of cyclic seta:, it is shown that #L less than or equal to 2nk - ((2k+1)(2)) always holds and that #L equals 2nk - ((2k+1)(2)) if and only if there is no collection L' of lines in H with L subset of or equal to L', k(L') = k(L) and C(L') = C(L).

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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MATHEMATICS

MATEMATIK

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